Editing Density matrix (section)

{{short description|Mathematical tool in quantum physics}}
{{Quantum mechanics|cTopic=Advanced topics}}
In [[quantum mechanics]], a '''density matrix''' (or '''density operator''') is a [[Matrix (mathematics)|matrix]] used in calculating the [[probabilities]] of the outcomes of [[Measurement in quantum mechanics|measurements]] performed on [[physical system]]s.<ref>{{Cite book |last=Shankar |first=Ramamurti |title=Principles of quantum mechanics |date=2014 |publisher=Springer |isbn=978-0-306-44790-7 |edition=2. ed., [19. corrected printing] |location=New York, NY}}</ref> It is a generalization of the state vectors or [[wavefunction]]s: while those can only represent [[pure state]]s, density matrices can also represent mixed states.<ref name=":0"/>{{rp|p=73}}<ref name="mikeandike" />{{rp|p=100}} These arise in quantum mechanics in two different situations:
# when the preparation of a system can randomly produce different pure states, and thus one must deal with the statistics of possible preparations, and
# when one wants to describe a physical system that is [[quantum entanglement|entangled]] with another, without describing their combined state. This case is typical for a system interacting with some environment (e.g. [[quantum decoherence|decoherence]]). In this case, the density matrix of an entangled system differs from that of an ensemble of pure states that, combined, would give the same statistical results upon measurement.

Density matrices are thus crucial tools in areas of quantum mechanics that deal with mixed states, such as [[quantum statistical mechanics]], [[open quantum system]]s and [[quantum information]].